Is it ethical to create a chatbot to answer questions on Stack Overflow?
Yes, it is possible, and has actually been done in the past.

The University of Antwerp created a bot to answer questions (this is the technical report). It focused on the git tag only though (even though it did answer one mysql question).

Its accuracy was pretty good, and the bots in the tests did earn some reputation. So I assume it is possible.

But do note that the last bot in the tests revealed that it was a bot, and thus got banned. So if you reveal that the account you are running the bot on is a bot, there is a high chance that it will get banned.